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Matthew Butterick 6 years ago
parent 91e0399ed6
commit b94c278f4b
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csp/hacs.rkt
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#lang debug racket
(require racket/generator sugar graph rackunit math)
(provide (all-defined-out))
(struct $csp ([vars #:mutable]
[constraints #:mutable]) #:transparent)
(struct $constraint (names proc) #:transparent)
(struct $var (name vals) #:transparent)
(define $var-name? symbol?)
(struct $avar $var () #:transparent)
(struct inconsistency-signal (csp) #:transparent)
(define/contract (check-name-in-csp! caller csp name)
(symbol? $csp? $var-name? . -> . void?)
(define names (map $var-name ($csp-vars csp)))
(unless (memq name names)
(raise-argument-error caller (format "one of these existing csp var names: ~v" names) name)))
(define/contract ($csp-var csp name)
($csp? $var-name? . -> . $var?)
(check-name-in-csp! '$csp-var csp name)
(for/first ([var (in-list ($csp-vars csp))]
#:when (eq? name ($var-name var)))
var))
(define/contract ($csp-vals csp name)
($csp? $var-name? . -> . (listof any/c))
(check-name-in-csp! '$csp-vals csp name)
($var-vals ($csp-var csp name)))
(define order-domain-values values)
(define (assign-val csp name val)
($csp
(for/list ([var ($csp-vars csp)])
(if (eq? name ($var-name var))
($avar name (list val))
var))
($csp-constraints csp)))
(define current-select-variable (make-parameter #f))
(define current-order-values (make-parameter #f))
(define current-inference (make-parameter #f))
(define (first-unassigned-variable csp)
(for/first ([var ($csp-vars csp)]
#:unless ($avar? var))
var))
(check-equal? (first-unassigned-variable ($csp (list ($var 'a (range 3)) ($var 'b (range 3))) null)) ($var 'a (range 3)))
(check-equal? (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($var 'b (range 3))) null)) ($var 'b (range 3)))
(check-false (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($avar 'b (range 3))) null)))
(define first-domain-value values)
(define (no-inference csp name) csp)
(define (forward-check csp aname)
(define aval (first ($csp-vals csp aname)))
(define (filter-vals var)
(match-define ($var name vals) var)
(define new-vals
(match (for*/list ([constraint (in-list ($csp-constraints csp))]
[cnames (in-value ($constraint-names constraint))]
#:when (and (memq aname cnames) (memq name cnames)))
constraint)
[(list) vals]
[constraints
(for*/list ([val (in-list vals)]
[constraint (in-list constraints)]
[cnames (in-value ($constraint-names constraint))]
#:when (cond
[(eq? (first cnames) name)
(($constraint-proc constraint) val aval)]
[(eq? (second cnames) name)
(($constraint-proc constraint) aval val)]
[else #true]))
val)]))
(unless (pair? new-vals) (raise (inconsistency-signal csp)))
new-vals)
($csp
(for/list ([var ($csp-vars csp)])
(if ($avar? var)
var
($var ($var-name var) (filter-vals var))))
($csp-constraints csp)))
(check-equal?
($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($var 'b (range 2))) null) 'a))
(list ($avar 'a '(1)) ($var 'b '(0 1))))
(check-equal?
;; no inconsistency because b≠c not checked (because fc is relative to a)
($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($var 'b (range 2)) ($var 'c '(0)))
(list ($constraint '(a b) (negate =))
($constraint '(b c) (negate =)))) 'a))
(list ($avar 'a '(1)) ($var 'b '(0)) ($var 'c '(0))))
(check-equal?
;; no inconsistency because a≠b not checked (because fc ignores a, which is already assigned)
($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($avar 'b '(1)) ($var 'c (range 2)))
(list ($constraint '(a b) (negate =))
($constraint '(b c) (negate =)))) 'b))
(list ($avar 'a '(1)) ($avar 'b '(1)) ($var 'c '(0))))
(check-exn inconsistency-signal?
(λ () ($csp-vars (forward-check ($csp (list ($avar 'a '(1))
($var 'b '(1)))
(list ($constraint '(a b) (negate =)))) 'a))))
(define/contract (backtrack-solution-generator csp
[select-unassigned-variable (or (current-select-variable) first-unassigned-variable)]
[order-domain-values (or (current-order-values) first-domain-value)]
[inference (or (current-inference) no-inference)])
(($csp?) (procedure? procedure? procedure?) . ->* . generator?)
(generator ()
(let backtrack ([csp csp])
(match (select-unassigned-variable csp)
[#false (yield csp)]
[($var name vals)
(for ([val (in-list (order-domain-values vals))])
(with-handlers ([inconsistency-signal? void])
(let* ([csp (assign-val csp name val)]
[csp (inference csp name)])
(backtrack csp))))]))))
(define/contract (solve* csp [finish-proc $csp-vars][solution-limit +inf.0])
(($csp?) (procedure? integer?) . ->* . (listof any/c))
(for/list ([solution (in-producer (backtrack-solution-generator csp) (void))]
[idx (in-range solution-limit)])
(finish-proc solution)))
(define/contract (solve csp [finish-proc $csp-vars])
(($csp?) (procedure?) . ->* . (or/c #false any/c))
(match (solve* csp finish-proc 1)
[(list solution) solution]
[else #false]))
(define (<> a b) (not (= a b)))
(define (neq? a b) (not (eq? a b)))
(parameterize ([current-inference forward-check])
(time (solve* ($csp (list ($var 'a (range 3))
($var 'b (range 3))
($var 'c (range 3)))
(list ($constraint '(a b) <>)
($constraint '(a c) <>)
($constraint '(b c) <>))))))
(parameterize ([current-inference forward-check])
(define vds (for/list ([k '(wa nsw t q nt v sa)])
($var k '(red green blue))))
(define cs (list
($constraint '(wa nt) neq?)
($constraint '(wa sa) neq?)
($constraint '(nt sa) neq?)
($constraint '(nt q) neq?)
($constraint '(q sa) neq?)
($constraint '(q nsw) neq?)
($constraint '(nsw sa) neq?)
($constraint '(nsw v) neq?)
($constraint '(v sa) neq?)))
(define csp ($csp vds cs))
(check-equal? (time (length (solve* csp))) 18))
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